library(plotly)
Attaching package: ‘plotly’
The following object is masked from ‘package:ggplot2’:
last_plot
The following object is masked from ‘package:stats’:
filter
The following object is masked from ‘package:graphics’:
layout
#########################################################################
###############function to create data set 2
cd1 <- function() {
t <- c(rep(0,100), rep(1,100))
x1 <- runif(200, 0,5) + t
x2 <- runif(200, 0,5) + t
x3 <- rep(c(rep("A",25), rep("B",25),rep("C",25), rep("D",25)),2)
# t <- c(rep("C",100),rep("T",100))
y <- 2*t + x1 + x2 #+ rnorm(200)
d <- list(x1=x1,x2=x2,x3=x3,t=t,y=y) %>% as.data.frame()
return(d)
}
dists <- function(data, form.t=NULL, model.t=NULL, form.y=NULL, model.y=NULL) {
#get the response variable from the formula
t = all.vars(form.t)[1]
#check the response is binary for logistic regression
if(all(as.numeric(data[t] == data[1,t]) %in% c(0,1))) {
data[t] <- as.numeric(data[t] != data[1,t])
}
#calculate the propensity score using logistic regression
if (is.null(model.t)){
prop.s <- glm(form.t, data=data, family = "binomial") %>% fitted()
}
dt <- cbind(idx= str_pad(row.names(data), nchar(nrow(data)), pad = "0"), data, prop.s)
dt <- dt %>% mutate(prop.wt=ifelse(t==1, 1/prop.s,1/(1-prop.s)))
Q <- quantile(dt$prop.s, prob=seq(from=0,to=1,by=0.2),na.rm=TRUE)
dt$prop.st <- cut(dt$prop.s, breaks = Q, labels = 1:5, include.lowest = TRUE)
return(dt)
}
d1 <- dists(form.t=t ~ x1 + x2, data=cd1())
# a <- glm(t ~ x1 + x2, data=d1, family = "binomial")
# m1 <- glm(ifelse(t=="C",0,1)~x1+x3, data=d1)
# a$model
#
# all.vars(a$terms)
#
# lm(y~t, data = d1)
# lm(y~t, weights = d1$prop.w, data = d1)
#
#
# summary(d1$prop.s)
#
# typeof(a)
# a %>% predict(newdata=d1, type = "response") == a$fitted.values
data <- cd1()
ggplot(data, aes(x1, x2, color=t)) + geom_point()

NA
NA
NA
NA
matches <- dist.matches(f=f, data=mdata)
Error in dist.matches(f = f, data = mdata) :
unused arguments (f = f, data = mdata)
Line <- gvisScatterChart(data[c("x1","x2", "t")],
options=list(
legend="right",
title="Hello World",
titleTextStyle="{color:'red',
fontName:'Courier',
fontSize:16}",
backgroundColor="#D3D3D3",
vAxis="{gridlines:{color:'red', count:3}}",
hAxis="{title:'X1', titleTextStyle:{color:'blue'}}",
series="[{color:'green', targetAxisIndex: 0},
{color: 'orange',targetAxisIndex:1}]",
vAxes="[{title:'val1'}, {title:'val2'}]",
legend="bottom",
curveType="function",
width=500,
height=500
), chartid = 55555)
plot(Line)
df <- gapminder
fig <- mdata %>%
plot_ly(
x = ~x1,
y = ~x2,
# size = ~pop,
color = ~c("No","Yes")[factor(t)],
# text = ~color,
frame = ~prop.st,
# text = paste0(round(~x1,2), ", ",round(~x2,2)),
hovertemplate = '%{color}: %{x:.2f}, %{y:.2f}<extra></extra>',
# hoverinfo = "text",
type = 'scatter',
mode = 'markers'
)
# fig <- fig %>% layout(
#
# xaxis = list(
#
# type = "log"
#
# )
#
# )
print(fig)
Warning in RColorBrewer::brewer.pal(N, "Set2") :
minimal value for n is 3, returning requested palette with 3 different levels
Warning in RColorBrewer::brewer.pal(N, "Set2") :
minimal value for n is 3, returning requested palette with 3 different levels
Warning in RColorBrewer::brewer.pal(N, "Set2") :
minimal value for n is 3, returning requested palette with 3 different levels
Warning in RColorBrewer::brewer.pal(N, "Set2") :
minimal value for n is 3, returning requested palette with 3 different levels
NULL
```r
f1 <- y ~ x2 * x1 * I(x1*x2) * I(x1^2) * I(x2^2) * I(x1^2*x2) * I(x1*x2^2) * I(x1^3) * I(x2^3)
output <- NULL
f1.t <- paste(f1[[2]],f1[[1]],\t\,c(\\,paste(\+\,labels(terms(f1)))))
# f1.t <- \y ~ t + x1 + x2\
# f1.t <- str_replace_all(f1.t, \:\, \+\)
f1.l <- lapply(f1.t,function(x) lm(x, data=d1))
# f1.s <- sapply(f1.t,function(x) lm(x, data=d1, weights= d1$prop.wt))
f1.est <- sapply(1:length(f1.l), function(x) f1.l[[c(x,1,2)]])
output <- rbind(output, cbind(mod=\Vanilla\,var=var(f1.est),max=max(f1.est), av=mean(f1.est)))
plot(f1.est, type = \l\)
# [1] 0.03991049
# [1] 4.200924
f1.l <- lapply(f1.t,function(x) lm(x, data=d1, weights= d1$prop.wt))
# f1.s <- sapply(f1.t,function(x) lm(x, data=d1, weights= d1$prop.wt))
f1.est <- sapply(1:length(f1.l), function(x) f1.l[[c(x,1,2)]])
# var(f1.est) #[[1]][2]
# max(f1.est) #[[1]][2]
output <- rbind(output, cbind(\Weighted\,var(f1.est), max(f1.est),
av=mean(f1.est)))
plot(f1.est, type = \l\)
# [1] 0.005683825
# [1] 2.525635
v <- NULL
for (i in 1:5){
f1.l <- lapply(f1.t,function(x) lm(x, data=d1[d1$prop.st==i,] ))
# f1.s <- sapply(f1.t,function(x) lm(x, data=d1, weights= d1$prop.wt))
# f1.l[[98]]
f1.est <- sapply(1:length(f1.l), function(x) f1.l[[c(x,1,2)]])
v <- rbind(v,cbind(variance=var(f1.est), max=max(f1.est), av=mean(f1.est)))
}
output <- rbind(output, cbind(\Stratified\,apply(v, 2, mean)%>%t())) %>%
as.data.frame()
# d1 %>% select(prop.st, t) %>% group_by_all() %>% mutate(n=n()) %>% unique()
plot(f1.est, type = \l\)
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```r
```r
df1 <- full_join(d1,d1,by=character(),suffix = c(\\, \.y\)) %>% filter(t != t.y) %>% mutate(p.dist=abs(prop.s - prop.s.y))
p.matches <- NULL
# m.matches <- NULL
p.ids <- list(idx=NULL,idx.y=NULL)
# m.ids <- list(id=NULL,s_id=NULL)
for (i in 1:(nrow(df1))) {
if (nrow(df1 %>% filter(!idx.y %in% p.ids$idx.y, !idx %in% p.ids$idx))!=0) {
p <- df1 %>% filter(!idx.y %in% p.ids$idx.y, !idx %in% p.ids$idx) %>%
filter(p.dist == min(p.dist))
p.matches <- rbind(p.matches, p)
p.ids <- p.matches[c(\idx\, \idx.y\)]
# m <- df3 %>% filter(!s_id %in% m.ids$s_id, !id %in% m.ids$id) %>%
# filter(m.dist == min(m.dist))
# m.matches <- rbind(m.matches, m)
# m.ids <- m.matches[c(\id\, \s_id\)]
}
}
dm <- as.matrix(p.matches[,c('x1','x2')]-p.matches[,c('x1.y','x2.y')])
#covariance matrix
c <- cov(d1[,c('x1','x2')])
# solve (covariance matrix) %*% x = d for x
cov.d <- sapply(1:nrow(p.matches), function(x) solve(c,dm[x,])) %>% t()
# Mahalanobis calculation forced in two steps
p.matches$m.dist <- apply(dm*cov.d, 1, sum)
p.matches %>% rowwise() %>%
mutate(a=x1-x1.y, b=x2-x2.y,
m.d = sum(c(a,b)*solve(cov(d1[,c('x1','x2')]), c(a,b)))) %>% select(-a, -b)
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```r
```r
# join(d1,p.matches,\\)
ests <- NULL
b <- NULL
for (i in seq(1,(nrow(p.matches)-9),by=2)){
data <- p.matches %>% arrange(desc(p.dist),t) %>% .[i:nrow(p.matches),]
bals <- bal.tab(t ~ x1 + x2, data = data,
distance = \prop.s\, s.d.denom = \treated\)
b <- rbind(b,list(x1.bal = bals$Balance[2,2], x2.bal = bals$Balance[1,2]) %>%
as.data.frame())
f1.l <- lapply(f1.t,function(x) lm(x, data=data))
# f1.s <- sapply(f1.t,function(x) lm(x, data=d1, weights= d1$prop.wt))
# f1.l[[98]]
f1.est <- sapply(1:length(f1.l), function(x) f1.l[[c(x,1,2)]])
ests <- rbind(ests,cbind(n=i,variance=var(f1.est), max=max(f1.est), av=mean(f1.est)))
}
ests <- ests %>% as.data.frame()
output <- output %>% as.data.frame()
colnames(output)<- c(\model\, \vars\, \max.val\, \av\)
output$vars <- output$vars %>% as.numeric()
output$max.val <- output$max.val %>% as.numeric()
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```r
```r
ggplot(p.matches, aes(x1,x2, color = as.factor(t))) +
annotate(\rect\, xmin=0, xmax=5, ymin=0, ymax=5, alpha=0.1, fill=\blue\) +
annotate(\rect\, xmin=1, xmax=6, ymin=1, ymax=6, alpha=0.1, fill=\red\) +
scale_color_manual(values=c(\blue\, \red\), name=\Group\, labels = c(\Control\,\Treat\)) +
geom_segment(data=p.matches[p.matches$t==0,],
aes(x=x1,xend=x1.y,y=x2,yend=x2.y,
alpha=cut(rank(p.dist),4,
labels=c(1,2,3,4))),
color= \black\, arrow = arrow(length = unit(0.2,\cm\))) +
scale_alpha_discrete(name=\Cuts\, labels=c(\1st\, \2nd\, \3rd\, \4th\), range = c(1,0.1)) +
geom_point() + theme_classic()
ggplot(p.matches[p.matches$t==0,], aes(prop.s,prop.s.y, color=p.dist)) +
geom_abline(slope=1) + geom_point() + theme_classic() + lims(x=c(0,1),y=c(0,1))
ggplot(p.matches[p.matches$t==0,], aes(prop.s,prop.wt, color=prop.st)) +
geom_point(alpha=0.7) + theme_classic()# + lims(x=c(0,1),y=c(0,1))
ggplot(p.matches[p.matches$t==0,], aes(p.dist, m.dist, color=prop.st)) +
geom_point(alpha=0.7) + theme_classic()# + lims(x=c(0,1),y=c(0,1))
ggplot(p.matches[p.matches$t==0,], aes(prop.s,m.dist, color=prop.st)) +
geom_point(alpha=0.7) + theme_classic()# + lims(x=c(0,1),y=c(0,1))
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```r
```r
ggarrange(
ggplot(ests, aes(n, variance)) + geom_line() +
geom_hline(data = output, aes(yintercept=vars, color=model)) +
labs(x=\Number of units removed\, y=\Average estimate variance\),
ggplot(ests, aes(n, max)) + geom_line() +
geom_hline(data = output, aes(yintercept=max.val, color=model)) +
labs(x=\Number of units removed\, y=\Maximum estimate\),
ggplot(ests, aes(n, av)) + geom_line() +
geom_hline(data = output, aes(yintercept=as.numeric(av), color=model)) +
labs(x=\Number of units removed\, y=\Average estimate\),
common.legend = T, legend = \bottom\
) %>% annotate_figure(top = \Output for 512 models including second and third order interactions\)
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```r
```r
# covs <- subset(p.matches, select = c(x1, x2, t))
#
# bal.tab(covs, treat = p.matches$t)
# bal.tab(covs, treat = p.matches$t, weights = p.matches$prop.wt)
# bals <- bal.tab(t ~ x1 + x2, data = p.matches, distance = \prop.s\, s.d.denom = \treated\)
# bals$Balance[c(2:nrow(bals$Balance)),2]
bal.wt <- bal.tab(t ~ x1 + x2, data = p.matches, weights = \prop.wt\,
distance = \prop.s\, s.d.denom = \treated\, unbal=T)$Balance
# Type Diff.Adj
# prop.s Distance 0.0691
# x1 Contin. 0.0529
# x2 Contin. 0.0932
bal.strat <- bal.tab(t ~ x1 + x2, data = p.matches, subclass = \prop.st\,
distance = \prop.s\, s.d.denom = \treated\,
which.subclass = .all, subclass.summary = TRUE)$Balance
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```r
```r
ggarrange(
ggplot(b, aes(x=row(b)[,1])) + geom_line(aes(y=x1.bal, color=\Matched\)) +
geom_hline(aes(yintercept=bal.wt[2,3], color=\Weighted\), ) +
geom_hline(aes(yintercept=bal.strat[2,3], color=\Stratified\)) +
theme_classic() + theme(legend.position = \right\) +
geom_ribbon(aes(ymin=-0.1,ymax=0.1), alpha=0.2) +
scale_color_manual(values = c(\black\, \darkblue\, \blue\),
name = \Method\) + labs(title=\x1\,x=\\,y=\\),
ggplot(b, aes(x=row(b)[,1])) + geom_line(aes(y=x2.bal, color=\x2 Match\)) +
geom_hline(aes(yintercept=bal.wt[3,3], color=\x2 Wt\)) +
geom_hline(aes(yintercept=bal.strat[3,3], color=\x2 Strat\)) +
geom_ribbon(aes(ymin=-0.1,ymax=0.1), alpha=0.2) +
theme_classic() + theme(legend.position = \right\) +
scale_color_manual(values = c(\black\, \blue\, \darkred\),
name = \Covariate\) + labs(title=\x2\,x=\\,y=\\),
common.legend = T, legend = \top\
) %>% annotate_figure(top = \Covariate balance by difference in standarised means\,
left = \Standardised mean difference\,
bottom = \Number of pairs removed\)
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```r
```r
# for (i in 1:200) {
# sapply(200, function(x) for(i in 1:x) {mean(rnorm(200))})
# }
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```r
```r
distance <- fitted(glm(treat~age+educ,lalonde, family=\binomial\))
sprobs <- seq(0, 1, length.out = round(6) + 1)
quantile(distance[lalonde$treat==1], probs = sprobs, na.rm = TRUE)
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```r
optmatch::match_on(distance, z=lalonde$treat)
An object of class "DenseMatrix"
control
treatment 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200
1 0.0344197445 0.0544716613 0.0653984572 0.022009534 0.0552959617 0.0025286797 0.0246904028 0.0859393864 0.007008826 0.010202874 0.0248871414 0.032257993 0.009930094 0.0393595932 0.078239007
2 0.0364328109 0.0163808942 0.0054540982 0.092862089 0.0155565937 0.0733812351 0.0461621526 0.0150868309 0.077861382 0.081055430 0.0957396968 0.038594563 0.060922461 0.0314929622 0.007386452
control
treatment 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215
1 0.034868512 0.0552959617 0.0401606405 0.010913833 0.006592504 0.046563399 0.0409629647 0.0058493302 0.045976877 0.0133687600 0.0423573652 0.002005214 0.015105517 0.076127653 0.0393595932
2 0.105721067 0.0155565937 0.0306919150 0.081766388 0.064260051 0.024289157 0.0298895907 0.0650032252 0.116829432 0.0842213155 0.0284951903 0.068847341 0.085958073 0.005275098 0.0314929622
control
treatment 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230
1 0.0767549377 0.056728339 0.0493862865 0.037979008 0.0544716613 0.0493862865 0.014608307 0.0596040046 0.053753811 0.023017835 0.0752742364 0.0496032463 0.0596040046 0.0805856355 0.015925664
2 0.0059023823 0.014124217 0.0214662689 0.108831563 0.0163808942 0.0214662689 0.056244248 0.0112485508 0.124606367 0.093870391 0.0044216810 0.0212493091 0.0112485508 0.0097330801 0.054926892
control
treatment 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245
1 0.0859393864 0.089821929 0.0596040046 0.0393595932 0.0859393864 0.031101061 0.0610472562 0.0128505183 0.010202874 0.019902128 0.0338383126 0.079096301 0.029529804 0.0058493302 0.0524422100
2 0.0150868309 0.018969374 0.0112485508 0.0314929622 0.0150868309 0.039751495 0.0098052992 0.0837030737 0.081055430 0.050950427 0.0370142428 0.008243745 0.041322751 0.0650032252 0.0184103455
control
treatment 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260
1 0.004020805 0.0708525554 0.016127944 0.008441925 0.051436026 0.0487874847 0.0267457681 0.06457150 0.0413391937 0.0415528334 0.038631920 0.0443486785 0.0493862865 0.056728339 0.008251782
2 0.066831750 0.0000000000 0.054724611 0.079294480 0.122288581 0.0220650708 0.0975983235 0.13542406 0.0295133617 0.0292997220 0.109484476 0.0265038769 0.0214662689 0.014124217 0.079104338
control
treatment 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275
1 0.0544716613 0.06821907 0.008251782 0.077382826 0.0641671299 0.0700061951 0.0596040046 0.0639445018 0.000000000 0.012143422 0.0883125844 0.050977968 0.091334442 0.103130260 0.036591195
2 0.0163808942 0.13907163 0.079104338 0.006530270 0.0066854255 0.0008463604 0.0112485508 0.0069080536 0.070852555 0.082995977 0.0174600290 0.121830523 0.020481887 0.032277704 0.034261360
control
treatment 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290
1 0.0399475884 0.0737969247 0.072323024 0.043762994 0.0596040046 0.043762994 0.0647824766 0.0859393864 0.0443486785 0.0426495738 0.06587304 0.0967697159 0.0805856355 0.0426495738 0.0805856355
2 0.0309049670 0.0029443692 0.001470469 0.114615549 0.0112485508 0.114615549 0.0060700789 0.0150868309 0.0265038769 0.1135021292 0.13672559 0.0259171605 0.0097330801 0.1135021292 0.0097330801
control
treatment 291 292 293 294 295 296 297 298 299 300 301 302 303 304
1 0.0138505243 0.091334442 0.0280985437 0.0850734147 0.0859393864 0.058167978 0.0457522991 0.0691609868 0.0387722879 0.0844383142 0.0393595932 0.0700061951 0.0844383142 0.0267457681
2 0.0570020311 0.020481887 0.0989510991 0.0142208593 0.0150868309 0.129020534 0.0251002564 0.0016915686 0.0320802675 0.0135857588 0.0314929622 0.0008463604 0.0135857588 0.0975983235
control
treatment 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319
1 0.0250683014 0.0508033402 0.0381856737 0.0596040046 0.0967697159 0.0350018758 0.0493862865 0.0952460701 0.0575559600 0.0700061951 0.0532996840 0.091334442 0.067079651 0.057111949 0.089821929
2 0.0959208569 0.0200492152 0.0326668817 0.0112485508 0.0259171605 0.0358506796 0.0214662689 0.0243935146 0.0132965955 0.0008463604 0.1241522394 0.020481887 0.003772904 0.127964504 0.018969374
control
treatment 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334
1 0.0829404943 0.0844383142 0.0805856355 0.010202874 0.0030617991 0.0868064317 0.0279190820 0.078466777 0.0700061951 0.010481106 0.0967697159 0.0297602314 0.003824400 0.0618811225 0.057111949
2 0.0120879389 0.0135857588 0.0097330801 0.081055430 0.0739143545 0.0159538763 0.0987716374 0.007614222 0.0008463604 0.060371449 0.0259171605 0.1006127868 0.067028155 0.0089714330 0.127964504
control
treatment 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349
1 0.0737969247 0.091334442 0.07307488 0.0805856355 0.0647824766 0.005304578 0.0874436877 0.0946019439 0.0937255052 0.0443486785 0.0624940950 0.012143422 0.062787644 0.049892943 0.0946019439
2 0.0029443692 0.020481887 0.14392743 0.0097330801 0.0060700789 0.065547977 0.0165911322 0.0237493885 0.0228729498 0.0265038769 0.0083584605 0.082995977 0.133640199 0.120745498 0.0237493885
control
treatment 350 351 352 353 354 355 356 357 358 359 360 361 362 363
1 0.0344197445 0.0275978248 0.0737969247 0.0493862865 0.0552959617 0.0835742152 0.099178152 0.0138862389 0.092208046 0.0596040046 0.0799547031 0.0928500992 0.089821929 0.0752742364
2 0.0364328109 0.0432547306 0.0029443692 0.0214662689 0.0155565937 0.0127216597 0.028325597 0.0847387943 0.021355491 0.0112485508 0.0091021477 0.0219975438 0.018969374 0.0044216810
control
treatment 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378
1 0.0952460701 0.077610299 0.0647824766 0.0952460701 0.099178152 0.099178152 0.0937255052 0.06661790 0.0952460701 0.099178152 0.0544716613 0.016320532 0.0967697159 0.0714746749 0.090693717
2 0.0243935146 0.006757744 0.0060700789 0.0243935146 0.028325597 0.028325597 0.0228729498 0.13747046 0.0243935146 0.028325597 0.0163808942 0.087173087 0.0259171605 0.0006221195 0.019841162
control
treatment 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393
1 0.0415528334 0.0140518189 0.0952460701 0.0145898418 0.0835742152 0.036591195 0.021440475 0.043121480 0.0814459497 0.0136493259 0.033410401 0.104669382 0.0967697159 0.012143422 0.103130260
2 0.0292997220 0.0568007365 0.0243935146 0.0854423972 0.0127216597 0.034261360 0.049412081 0.113974036 0.0105933943 0.0572032296 0.104262956 0.033816827 0.0259171605 0.082995977 0.032277704
control
treatment 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408
1 0.104669382 0.0346304230 0.0859393864 0.0853034947 0.101594087 0.0844383142 0.007884573 0.016687154 0.030105994 0.0976496996 0.1000608899 0.0287461457 0.091334442 0.012143422 0.058613765
2 0.033816827 0.0362221324 0.0150868309 0.0144509392 0.030741531 0.0135857588 0.062967982 0.054165401 0.040746561 0.0267971442 0.0292083345 0.0421064098 0.020481887 0.082995977 0.129466321
control
treatment 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423
1 0.008966595 0.090693717 0.010202874 0.100709622 0.0915665540 0.091334442 0.0536485817 0.0952460701 0.0889511946 0.0859393864 0.0928500992 0.0589940729 0.0493862865 0.0868064317 0.06500611
2 0.079819150 0.019841162 0.081055430 0.029857066 0.0207139986 0.020481887 0.0172039737 0.0243935146 0.0180986392 0.0150868309 0.0219975438 0.0118584825 0.0214662689 0.0159538763 0.13585867
control
treatment 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438
1 0.0952460701 0.104669382 0.0967697159 0.033410401 0.0835742152 0.000732180 0.0820782812 0.022514069 0.0891825426 0.0114349122 0.077837852 0.0260383370 0.103130260 0.1000608899 0.076127653
2 0.0243935146 0.033816827 0.0259171605 0.104262956 0.0127216597 0.070120375 0.0112257257 0.093366624 0.0183299871 0.0822874676 0.006985297 0.0448142185 0.032277704 0.0292083345 0.005275098
control
treatment 439 440 441 442 443 444 445 446 447 448 449 450 451 452
1 0.0752742364 0.068541180 0.0961242884 0.0746483845 0.0937255052 0.0647824766 0.0647824766 0.103130260 0.0799547031 0.0255681533 0.0961242884 0.0853034947 0.0976496996 0.0835742152
2 0.0044216810 0.002311375 0.0252717330 0.0037958290 0.0228729498 0.0060700789 0.0060700789 0.032277704 0.0091021477 0.0964207088 0.0252717330 0.0144509392 0.0267971442 0.0127216597
control
treatment 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467
1 0.103130260 0.0714746749 0.103130260 0.100709622 0.043121480 0.022006538 0.0952460701 0.0700061951 0.0937255052 0.0883125844 0.1000608899 0.0473757512 0.104669382 0.099178152 0.099178152
2 0.032277704 0.0006221195 0.032277704 0.029857066 0.113974036 0.048846018 0.0243935146 0.0008463604 0.0228729498 0.0174600290 0.0292083345 0.0234768042 0.033816827 0.028325597 0.028325597
control
treatment 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482
1 0.0641671299 0.0393595932 0.099178152 0.053753811 0.0829404943 0.0071996172 0.0883125844 0.0952460701 0.0985306947 0.0693855400 0.029529804 0.0844383142 0.100709622 0.0532996840 0.047245634
2 0.0066854255 0.0314929622 0.028325597 0.124606367 0.0120879389 0.0780521727 0.0174600290 0.0243935146 0.0276781393 0.0014670154 0.041322751 0.0135857588 0.029857066 0.1241522394 0.118098190
control
treatment 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497
1 0.044872095 0.0138505243 0.0693855400 0.0493862865 0.031679174 0.060869179 0.0250683014 0.045157598 0.011785551 0.033410401 0.0737969247 0.0752742364 0.068541180 0.07674388 0.0573358510
2 0.115724650 0.0570020311 0.0014670154 0.0214662689 0.039173381 0.131721734 0.0959208569 0.025694957 0.059067004 0.104262956 0.0029443692 0.0044216810 0.002311375 0.14759644 0.0135167044
control
treatment 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512
1 0.0151655274 0.0737969247 0.029529804 0.091334442 0.0618811225 0.0058493302 0.0814459497 0.0641671299 0.009180777 0.0700061951 0.036591195 0.0604358000 0.0937255052 0.037979008 0.0820782812
2 0.0556870280 0.0029443692 0.041322751 0.020481887 0.0089714330 0.0650032252 0.0105933943 0.0066854255 0.061671778 0.0008463604 0.034261360 0.0104167554 0.0228729498 0.108831563 0.0112257257
control
treatment 513 514 515 516 517 518 519 520 521 522 523 524 525 526
1 0.0407495735 0.0850734147 0.0812171614 0.0647824766 0.0889511946 0.0823073606 0.0868064317 0.091334442 0.0874436877 0.091334442 0.0445635754 0.0502029595 0.0700061951 0.0814459497
2 0.0301029819 0.0142208593 0.0103646060 0.0060700789 0.0180986392 0.0114548051 0.0159538763 0.020481887 0.0165911322 0.020481887 0.0262889800 0.0206495959 0.0008463604 0.0105933943
control
treatment 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541
1 0.0829404943 0.0045637979 0.0077260788 0.0976496996 0.08061326 0.0387722879 0.091334442 0.005040552 0.103130260 0.099178152 0.0647824766 0.089821929 0.060709290 0.0868064317 0.008061540
2 0.0120879389 0.0662887575 0.0785786342 0.0267971442 0.15146582 0.0320802675 0.020481887 0.075893108 0.032277704 0.028325597 0.0060700789 0.018969374 0.131561845 0.0159538763 0.078914096
control
treatment 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556
1 0.0952460701 0.1000608899 0.079096301 0.07771755 0.001270624 0.0544716613 0.06821907 0.0532996840 0.101594087 0.103130260 0.0937255052 0.0133687600 0.101594087 0.103130260 0.0573358510
2 0.0243935146 0.0292083345 0.008243745 0.14857010 0.069581932 0.0163808942 0.13907163 0.1241522394 0.030741531 0.032277704 0.0228729498 0.0842213155 0.030741531 0.032277704 0.0135167044
control
treatment 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571
1 0.0814459497 0.0859393864 0.0952460701 0.038631920 0.0961242884 0.103130260 0.031679174 0.019902128 0.0151655274 0.0820782812 0.0379734621 0.091334442 0.0187761110 0.091334442 0.0859393864
2 0.0105933943 0.0150868309 0.0243935146 0.109484476 0.0252717330 0.032277704 0.039173381 0.050950427 0.0556870280 0.0112257257 0.0328790933 0.020481887 0.0520764445 0.020481887 0.0150868309
control
treatment 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586
1 0.07965223 0.089821929 0.0952460701 0.044403071 0.103130260 0.099178152 0.0032546278 0.009930094 0.06457150 0.043292142 0.103130260 0.0961242884 0.0522241111 0.0037867205 0.099178152
2 0.15050479 0.018969374 0.0243935146 0.115255627 0.032277704 0.028325597 0.0741071832 0.060922461 0.13542406 0.114144697 0.032277704 0.0252717330 0.0186284444 0.0746392760 0.028325597
control
treatment 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601
1 0.101594087 0.045509682 0.07674388 0.0850734147 0.104669382 0.0700061951 0.038631920 0.099178152 0.015992796 0.0937255052 0.06457150 0.099178152 0.0930826909 0.032080363 0.0151655274
2 0.030741531 0.116362237 0.14759644 0.0142208593 0.033816827 0.0008463604 0.109484476 0.028325597 0.086845351 0.0228729498 0.13542406 0.028325597 0.0222301355 0.102932918 0.0556870280
control
treatment 602 603 604 605 606 607 608 609 610 611 612 613 614
1 0.101594087 0.0493862865 0.06543996 0.0199399478 0.07576599 0.103130260 0.046563399 0.0624940950 0.0952460701 0.0490042020 0.089590375 0.0153674479 0.103130260
2 0.030741531 0.0214662689 0.13629251 0.0907925033 0.14661854 0.032277704 0.024289157 0.0083584605 0.0243935146 0.0218483535 0.018737820 0.0554851075 0.032277704
[ reached getOption("max.print") -- omitted 183 rows ]
Slot "call":
optmatch::match_on(x = distance, z = lalonde$treat)
dist()
---
title: "R Notebook"
output: html_notebook
---

```{r}
library(tidyverse)
library(MatchIt)
library(cem)
library(ggpubr)
library(cobalt)
library(plotly)
library(gapminder)

```



```{r}
#########################################################################
###############function to create data set 2
cd1 <- function() {
    
    t <- c(rep(0,100), rep(1,100))
    x1 <- runif(200, 0,5) + t
    x2 <- runif(200, 0,5) + t
    x3 <- rep(c(rep("A",25), rep("B",25),rep("C",25), rep("D",25)),2)
    # t <- c(rep("C",100),rep("T",100))
    y <- 2*t + x1 + x2 #+ rnorm(200)

    d <- list(x1=x1,x2=x2,x3=x3,t=t,y=y) %>% as.data.frame()

    return(d)
}


dists <- function(data, form.t=NULL, model.t=NULL, form.y=NULL, model.y=NULL) {
    
    #get the response variable from the formula
    t = all.vars(form.t)[1]
    
    #check the response is binary for logistic regression
    if(all(as.numeric(data[t] == data[1,t]) %in% c(0,1))) {
        data[t] <- as.numeric(data[t] != data[1,t])
    }
    
    #calculate the propensity score using logistic regression
    if (is.null(model.t)){
        prop.s <- glm(form.t, data=data, family = "binomial") %>% fitted()
    }
    
    
    
    dt <- cbind(idx= str_pad(row.names(data), nchar(nrow(data)), pad = "0"), data, prop.s)
    
    dt <- dt %>% mutate(prop.wt=ifelse(t==1, 1/prop.s,1/(1-prop.s)))
    
    Q <- quantile(dt$prop.s, prob=seq(from=0,to=1,by=0.2),na.rm=TRUE)
    dt$prop.st <- cut(dt$prop.s, breaks = Q, labels = 1:5, include.lowest = TRUE)
    
    return(dt)
}

d1 <- dists(form.t=t ~ x1 + x2, data=cd1())


# a <- glm(t ~ x1 + x2, data=d1, family = "binomial") 
# m1 <- glm(ifelse(t=="C",0,1)~x1+x3, data=d1)
# a$model
# 
# all.vars(a$terms)
# 
# lm(y~t, data = d1)
# lm(y~t, weights = d1$prop.w, data = d1)
# 
# 
# summary(d1$prop.s)
# 
# typeof(a)

# a %>% predict(newdata=d1, type = "response") == a$fitted.values

data <- cd1()

ggplot(data, aes(x1, x2, color=t)) + geom_point() 




```

```{r}
f <- t ~ x1 + x2
mdata <- dists(data, form.t = f)
matches <- dist.matches(f=f, data=mdata)
```



```{r}

Line <-  gvisScatterChart(data[c("x1","x2", "t")],
                       options=list(
                         legend="right",
                         title="Hello World",
                         titleTextStyle="{color:'red',
                                           fontName:'Courier',
                                           fontSize:16}",
                         backgroundColor="#D3D3D3",
                         vAxis="{gridlines:{color:'red', count:3}}",
                         hAxis="{title:'X1', titleTextStyle:{color:'blue'}}",
                         series="[{color:'green', targetAxisIndex: 0},
                                   {color: 'orange',targetAxisIndex:1}]",
                         vAxes="[{title:'val1'}, {title:'val2'}]",
                         legend="bottom",
                         curveType="function",
                         width=500,
                         height=500
                       ), chartid = 55555)
plot(Line)

```


```{r}

df <- gapminder 

fig <- mdata %>%

  plot_ly(

    x = ~x1, 

    y = ~x2, 

    # size = ~pop, 

    color = ~c("No","Yes")[factor(t)], 
    
    # text = ~color,

    frame = ~prop.st,

    # text = paste0(round(~x1,2), ", ",round(~x2,2)),
    
    hovertemplate = '%{color}: %{x:.2f}, %{y:.2f}<extra></extra>',

    # hoverinfo = "text",

    type = 'scatter',

    mode = 'markers'

  )

# fig <- fig %>% layout(
# 
#     xaxis = list(
# 
#       type = "log"
# 
#     )
# 
#   )


print(fig)

```



```{r}
f1 <- y ~ x2 * x1 * I(x1*x2) * I(x1^2) * I(x2^2) * I(x1^2*x2) * I(x1*x2^2) * I(x1^3) * I(x2^3)

output <- NULL


f1.t <- paste(f1[[2]],f1[[1]],"t",c("",paste("+",labels(terms(f1)))))

# f1.t <- "y ~ t + x1 + x2"

# f1.t <- str_replace_all(f1.t, ":", "+")


f1.l <- lapply(f1.t,function(x) lm(x, data=d1))

# f1.s <- sapply(f1.t,function(x) lm(x, data=d1, weights= d1$prop.wt))

f1.est <- sapply(1:length(f1.l), function(x) f1.l[[c(x,1,2)]])

output <- rbind(output, cbind(mod="Vanilla",var=var(f1.est),max=max(f1.est), av=mean(f1.est)))

plot(f1.est, type = "l")

# [1] 0.03991049
# [1] 4.200924

f1.l <- lapply(f1.t,function(x) lm(x, data=d1, weights= d1$prop.wt))

# f1.s <- sapply(f1.t,function(x) lm(x, data=d1, weights= d1$prop.wt))

f1.est <- sapply(1:length(f1.l), function(x) f1.l[[c(x,1,2)]])



# var(f1.est)  #[[1]][2]
# max(f1.est)  #[[1]][2]

output <- rbind(output, cbind("Weighted",var(f1.est), max(f1.est), 
                              av=mean(f1.est)))
plot(f1.est, type = "l")
# [1] 0.005683825
# [1] 2.525635

v <- NULL

for (i in 1:5){
    


f1.l <- lapply(f1.t,function(x) lm(x, data=d1[d1$prop.st==i,] ))

# f1.s <- sapply(f1.t,function(x) lm(x, data=d1, weights= d1$prop.wt))

# f1.l[[98]]

f1.est <- sapply(1:length(f1.l), function(x) f1.l[[c(x,1,2)]])

v <- rbind(v,cbind(variance=var(f1.est), max=max(f1.est), av=mean(f1.est)))

}

output <- rbind(output, cbind("Stratified",apply(v, 2, mean)%>%t())) %>%
    as.data.frame()
# d1 %>% select(prop.st, t) %>% group_by_all() %>% mutate(n=n()) %>% unique()
plot(f1.est, type = "l")

```



```{r}

df1 <- full_join(d1,d1,by=character(),suffix = c("", ".y")) %>% filter(t != t.y) %>% mutate(p.dist=abs(prop.s - prop.s.y))


p.matches <- NULL
# m.matches <- NULL
p.ids <- list(idx=NULL,idx.y=NULL)
# m.ids <- list(id=NULL,s_id=NULL)

for (i in 1:(nrow(df1))) {
    
    if (nrow(df1 %>% filter(!idx.y %in% p.ids$idx.y, !idx %in% p.ids$idx))!=0) {
    
    p <- df1 %>% filter(!idx.y %in% p.ids$idx.y, !idx %in% p.ids$idx) %>% 
          filter(p.dist == min(p.dist)) 
    p.matches <- rbind(p.matches, p)
    p.ids <- p.matches[c("idx", "idx.y")]
    
    # m <- df3 %>% filter(!s_id %in% m.ids$s_id, !id %in% m.ids$id) %>% 
    #       filter(m.dist == min(m.dist)) 
    # m.matches <- rbind(m.matches, m)
    # m.ids <- m.matches[c("id", "s_id")]
    }
    
}


dm <- as.matrix(p.matches[,c('x1','x2')]-p.matches[,c('x1.y','x2.y')])

#covariance matrix
c <- cov(d1[,c('x1','x2')])

# solve  (covariance matrix) %*% x = d for x
cov.d <- sapply(1:nrow(p.matches), function(x) solve(c,dm[x,])) %>% t()

# Mahalanobis calculation forced in two steps
p.matches$m.dist <- apply(dm*cov.d, 1, sum)


p.matches %>% rowwise() %>% 
    mutate(a=x1-x1.y, b=x2-x2.y,
           m.d = sum(c(a,b)*solve(cov(d1[,c('x1','x2')]), c(a,b)))) %>% select(-a, -b)


```



```{r}

# join(d1,p.matches,"")

ests <- NULL
b <- NULL

for (i in seq(1,(nrow(p.matches)-9),by=2)){
    
    data <- p.matches %>% arrange(desc(p.dist),t) %>% .[i:nrow(p.matches),]
    
    bals <- bal.tab(t ~ x1 + x2, data = data, 
                    distance = "prop.s", s.d.denom = "treated")

    b <- rbind(b,list(x1.bal = bals$Balance[2,2], x2.bal = bals$Balance[1,2]) %>% 
                   as.data.frame())
    
    f1.l <- lapply(f1.t,function(x) lm(x, data=data))
    
    # f1.s <- sapply(f1.t,function(x) lm(x, data=d1, weights= d1$prop.wt))
    
    # f1.l[[98]]
    
    f1.est <- sapply(1:length(f1.l), function(x) f1.l[[c(x,1,2)]])
    
    ests <- rbind(ests,cbind(n=i,variance=var(f1.est), max=max(f1.est), av=mean(f1.est)))

}

ests <- ests %>% as.data.frame()
output <- output %>% as.data.frame()

colnames(output)<- c("model", "vars", "max.val", "av")

output$vars <- output$vars %>% as.numeric()

output$max.val <- output$max.val %>% as.numeric()

```


```{r}
ggplot(p.matches, aes(x1,x2, color = as.factor(t))) + 
  annotate("rect", xmin=0, xmax=5, ymin=0, ymax=5, alpha=0.1, fill="blue") + 
  annotate("rect", xmin=1, xmax=6, ymin=1, ymax=6, alpha=0.1, fill="red") +
  scale_color_manual(values=c("blue", "red"), name="Group", labels = c("Control","Treat")) +
  geom_segment(data=p.matches[p.matches$t==0,],
               aes(x=x1,xend=x1.y,y=x2,yend=x2.y, 
                   alpha=cut(rank(p.dist),4,
                             labels=c(1,2,3,4))), 
               color= "black", arrow = arrow(length = unit(0.2,"cm"))) +
    scale_alpha_discrete(name="Cuts", labels=c("1st", "2nd", "3rd", "4th"), range = c(1,0.1)) +
  geom_point() + theme_classic() 


ggplot(p.matches[p.matches$t==0,], aes(prop.s,prop.s.y, color=p.dist)) + 
  geom_abline(slope=1) + geom_point() + theme_classic() + lims(x=c(0,1),y=c(0,1)) 

ggplot(p.matches[p.matches$t==0,], aes(prop.s,prop.wt, color=prop.st)) + 
 geom_point(alpha=0.7) + theme_classic()# + lims(x=c(0,1),y=c(0,1)) 

ggplot(p.matches[p.matches$t==0,], aes(p.dist, m.dist, color=prop.st)) + 
 geom_point(alpha=0.7) + theme_classic()# + lims(x=c(0,1),y=c(0,1)) 

ggplot(p.matches[p.matches$t==0,], aes(prop.s,m.dist, color=prop.st)) + 
 geom_point(alpha=0.7) + theme_classic()# + lims(x=c(0,1),y=c(0,1)) 

```




```{r}

ggarrange(
ggplot(ests, aes(n, variance)) + geom_line() + 
    geom_hline(data = output, aes(yintercept=vars, color=model)) +
    labs(x="Number of units removed", y="Average estimate variance"),

ggplot(ests, aes(n, max)) + geom_line() + 
    geom_hline(data = output, aes(yintercept=max.val, color=model)) +
    labs(x="Number of units removed", y="Maximum estimate"),

ggplot(ests, aes(n, av)) + geom_line() + 
    geom_hline(data = output, aes(yintercept=as.numeric(av), color=model)) + 
    labs(x="Number of units removed", y="Average estimate"),
common.legend = T, legend = "bottom"
) %>% annotate_figure(top = "Output for 512 models including second and third order interactions")

```


```{r}

# covs <- subset(p.matches, select = c(x1, x2, t))
# 
# bal.tab(covs, treat = p.matches$t)
# bal.tab(covs, treat = p.matches$t, weights = p.matches$prop.wt)

# bals <- bal.tab(t ~ x1 + x2, data = p.matches, distance = "prop.s", s.d.denom = "treated")

# bals$Balance[c(2:nrow(bals$Balance)),2]

bal.wt <- bal.tab(t ~ x1 + x2, data = p.matches, weights = "prop.wt",
        distance = "prop.s", s.d.denom = "treated", unbal=T)$Balance

#            Type Diff.Adj
# prop.s Distance   0.0691
# x1      Contin.   0.0529
# x2      Contin.   0.0932


bal.strat <- bal.tab(t ~ x1 + x2, data = p.matches, subclass = "prop.st",
        distance = "prop.s", s.d.denom = "treated", 
        which.subclass = .all, subclass.summary = TRUE)$Balance

```





```{r}

ggarrange(
ggplot(b, aes(x=row(b)[,1])) + geom_line(aes(y=x1.bal, color="Matched")) +
    geom_hline(aes(yintercept=bal.wt[2,3], color="Weighted"), ) +
    geom_hline(aes(yintercept=bal.strat[2,3], color="Stratified")) +
    theme_classic() + theme(legend.position = "right") +
    geom_ribbon(aes(ymin=-0.1,ymax=0.1), alpha=0.2) +
    scale_color_manual(values = c("black", "darkblue", "blue"), 
                       name = "Method") + labs(title="x1",x="",y=""),
ggplot(b, aes(x=row(b)[,1])) + geom_line(aes(y=x2.bal, color="x2 Match")) + 
    geom_hline(aes(yintercept=bal.wt[3,3], color="x2 Wt")) +
    geom_hline(aes(yintercept=bal.strat[3,3], color="x2 Strat")) +
    geom_ribbon(aes(ymin=-0.1,ymax=0.1), alpha=0.2) +
    theme_classic() + theme(legend.position = "right") +
    scale_color_manual(values = c("black", "blue", "darkred"), 
                       name = "Covariate") + labs(title="x2",x="",y=""),
common.legend = T, legend = "top"

) %>% annotate_figure(top = "Covariate balance by difference in standarised means", 
                      left = "Standardised mean difference",
                      bottom = "Number of pairs removed")
```


```{r}
# for (i in 1:200) {
# sapply(200, function(x) for(i in 1:x) {mean(rnorm(200))})
# }
```



```{r}
distance <- fitted(glm(treat~age+educ,lalonde, family="binomial"))

sprobs <- seq(0, 1, length.out = round(6) + 1)

quantile(distance[lalonde$treat==1], probs = sprobs, na.rm = TRUE)

```


```{r}
match <- matchit(treat~age+educ, lalonde, distance = "mahalanobis" , replace = T, m.order = "data")
# summary(match)

match.out <- match.data(match)
# summary(match.out)

# ggplot(match.out, aes(educ, age)) + geom_point(aes(color = as.factor(treat))) + geom_line(aes(group=subclass))

d.matrix <- optmatch::match_on(distance, z=lalonde$treat, standardization.scale=1)
d.matrix <- optmatch::match_on(match$formula, data = lalonde, method = "mahalanobis")
d.matrix2 <- optmatch::match_on(match$formula, data = lalonde, method = "mahalanobis", standardization.scale=1)


mat <-  dist.matches(d.matrix, replace = T, order = "data")


mat %>% 

# match$match.matrix==as.matrix(mat[['control']])

# cbind(mat, matchit = match$match.matrix) %>% filter(control!=matchit)

lalonde[mat$treatment,]
lalonde[mat$control,]

cbind(t=lalonde[mat$treatment,], c=lalonde[mat$control,],mat) %>% dim()


data.frame(IDs=c(mat$treatment, mat$control)) %>%  summarise(nIDs=n(), .groups = IDs)

t(table(c(mat$treatment, mat$control))) %>% dim()

table(mat$control)[mat$control] %>% dim()
```



```{r}

dist()

```

